Assessment Of Slow Deformations And Rapid Motions By

'Photogrammetric Week 05'Dieter Fritsch, Ed.Wichmann Verlag, Heidelberg 2005.Bamler et al.111Assessment of Slow Deformations and Rapid Motions by Radar InterferometryRICHARD BAMLER, BERT KAMPES, NICO ADAM, STEFFEN SUCHANDT,OberpfaffenhofenABSTRACTSpace-borne Synthetic Aperture Radar (SAR) interferometry is a powerful tool for measuring movements on ground byexploiting phase differences of SAR images taken at different time instances. Two technologies and their applicationsare described: 1) The persistent scatterer technique uses stacks of typically 100 images taken over up to 10 years forassessing slow deformation processes, e.g. land subsidence, at an accuracy of better than 1mm/year. 2) Along-trackinterferometry is used to measure the velocity of vehicles for traffic monitoring. The potential of TerraSAR-X, theGerman radar satellite to be launched in 2006, for interferometry is discussed.1. SAR INTERFEROMETRYSynthetic Aperture Rader (SAR) interferometry (InSAR) exploits the phase differences of two ormore complex-valued SAR images of the same area for information extraction about topography,temporal stability, or motion (for an InSAR review see, e.g. Bamler et al., 1998). A digital surfacemodel can be generated using the across-track InSAR configuration, i.e. where the two images aretaken by SARs spatially separated in the across-track direction by typically a few hundred meters(spatial baseline). Monitoring movements requires images taken at different time instances (temporal baseline). In the paper we will discuss two extremes: 1) the assessment of slow deformationprocesses, e.g. land subsidence, and 2) rapid motion measurements for traffic monitoring. In thefirst application up to hundred images spanning a period of about 10 years are used, while for thelatter application the time lag of the images is less than a millisecond.2. PERSISTENT SCATTERER INTERFEROMETRY (PSI)The observed phase at a pixel in an interferogram is related to the difference in measured distancesof a terrain element to the radar sensors at the times of the acquisitions. This difference in turn is amixture of displacement, topography, and atmospheric delay. In most InSAR applications it is assumed that the component of interest is dominantly present, while the other contributions can eitherbe estimated independently or practically neglected. Moreover, in most studies the coherence of theinterferogram (i.e., the precision of the phase observations) is relatively high, supporting interpretation. However, due to temporal and geometrical decorrelation (see, e.g., Gatelli et al., 1994; Zebkeret al., 1992), high coherence can not be expected in general, and long-term observations by traditional InSAR techniques are therefore often restricted to non-vegetated areas.In the late 1990s, the multi-image Permanent Scatterer (PS) technique was introduced (Ferretti etal., 1999). This technique offers a systematic processing strategy, capable of utilizing all archiveddata of a certain area, by creating a stack of differential interferograms that have a common masterimage. Instead of analyzing the phase in the spatial domain, the phase of isolated coherent points isanalyzed as a function of time and space. A detailed description of the PS technique can be found in(Colesanti et al., 2003a,b; Ferretti et al., 2000, 2001). The PS technique bypasses the problem ofgeometrical and temporal decorrelation by considering only point-like scatterers. Furthermore, byusing a large amount of data, the atmospheric signal is estimated and corrected for. It offers a con-

112Bamler et al.venient processing framework that enables the use of all acquired images (irrespective of baseline),and a parameter estimation strategy for interferograms with low spatial coherence.Once the PS technique had demonstrated that using a large number of images was a way to reduceatmospheric artifacts and to obtain highly precise estimates despite decorrelation, this sparked thedevelopment of a number of related techniques, e.g., Coherent Target Monitoring, InterferometricPoint Target Analysis, Stable Point Network Analysis, Small Baseline Subset Approach, and Corner Reflector Interferometry. These techniques partly seek to improve the PS technique using modified approaches, but also partly try to avoid disputes over the patent of the PS technique. The termPersistent Scatterer Interferometry (PSI) is now used to group techniques that analyze the phase oflong-time coherent scatterers.At DLR, the existing operational GENESIS (Generic SAR interferometric software) system hasbeen extended with PSI processing capability (Adam et al. 2003, 2004).2.1. The PSI estimation algorithmA general description of the PSI-GENESIS system is given in (Kampes and Adam, 2004). Thenovel displacement estimation algorithm used in the system is called “Spatio-Temporal Unwrapping Network” (STUN). The three-dimensional unwrapping of the observed wrapped data in thegenerated interferometric stack is based (i) on a parametric temporal displacement model and (ii) onspatial unwrapping. The displacement can be modeled by a constant rate, but this estimator is easilyextended to more complex displacement models, mainly because the integer ambiguity space issearched, and not the solution space of the displacement parameters. The STUN algorithm is described in detail in (Kampes, 2005). Key points are:The displacement is modeled for each stable scatterer using a linear combination of base functions.The coefficients of these base functions are estimated simultaneously with a topographic term, and,if desired, with terms accounting for the average atmospheric delay and the sub-pixel position of thePS point.The integer least-squares estimator is used, see (Kampes and Hanssen, 2004). The estimator is routinely used for resolving phase ambiguities of GPS observations, and has been adapted to the PSIcase.A variance components stochastic model is used to weight the observations. This model accountsfor random noise and varying atmospheric signal during the acquisition times.A variance components estimation is performed using the so-called PS candidates to obtain estimates for the precision of the double-differenced (in time and space) phase observations used during the parameter estimation.Alternative hypothesis tests are performed to identify incorrect estimations and to guarantee a consistent network.The sparse grid Minimum Cost Flow phase unwrapping algorithm (Eineder and Holzner, 1999) isapplied, and the unwrapped data are used during the final estimation.The variance-covariance matrix of the estimated parameters is obtained, describing the precision ofand correlation between the estimated parameters.2.2. Subsidence MonitoringPSI processing is particularly useful for the analysis of urban displacements, because many manmade objects have perpendicular edges or are metallic, which are likely to act as stable pointscatterers. Since the data of the ERS satellites are archived since 1992, PSI is a very practical tool toobtain information on these displacements, using these historic data.

Bamler et al.113DLR’s GENESIS-PSI system was used in the course of an ESA study on a test site near Marseille,France, which included rural and mountainous terrain. In this test site, mining activities have led tosurface subsidence. The displacement can be modeled by a linear displacements rate in this case.For the analysis, 79 ERS-1 and ERS-2 acquisition are used spanning from May 6, 1992, throughOctober 25, 2003. The master image of the stack was acquired on March 20, 1999. The processedarea is approximately 25 km by 40 km.The first step of the STUN algorithm is to estimate the error of the observed data. It is propagated tothe error of the estimated parameters. The correlation between the estimated parameters can be neglected in this case, the correlation coefficient is 0.03. The estimated standard deviation of the estimated topographic term is as low as 0.33 m and 0.19 mm/y for the estimated linear displacementrate. These values are valid for relative estimations between points 1500 m apart, and get larger forpoints further away, due to an increasing atmospheric difference signal with distance. Figure 1shows the estimated linear displacement rates. In general, the processed area is stable, except thedeforming area in the center with maximum average subsidence rates of 13 mm/y for the observedtime interval. The detected points lie in a network of opportunity, i.e., their location depends on thestability of the radar signature of the objects under a range of look angles. Displacement time seriesare shown in figure 2 for two points close to and in the subsidence area.2.3. Seasonal DeformationThe Las Vegas area is the second test site described in this paper. Las Vegas is one of the fastestgrowing metropolitan areas in the USA. Between 1990 and 2000 the population almost doubled. Inthe metropolitan area live 1.4 million people. Currently, the urbanized area is approximately 20km by 20 km. Las Vegas lies in a broad desert valley in southern Nevada. Mountains surroundingthe valley extend to 3500 m above the valley floor. The average annual precipitation varies significantly from year to year but typically is between 5 and 20 cm. The area undergoes large displacements, dominantly linear and locally seasonal of nature. The local subsidence is primarilycaused by groundwater withdrawal. Between 1948 and 1963 the center of the valley had subsided 1.0 m, and by 1980 1.5 m, and it still continues to do so, see also (Bell et al. 2002).For this area, 45 ERS-1 and ERS-2 acquisitions were available from April 21, 1992, to February 18,2000. The selected master image was acquired on June 13, 1997. Significant atmospheric signal isvisible in the interferograms.The displacement is modeled using a linear and two trigonometric base functions for describing adisplacement rate with a superimposed seasonal component of a one year period. The estimatedaverage displacement rate between 1992 and 2000 is depicted in figure 3. The background imageshows the average intensity of the 45 acquisitions. The NS-EW street pattern, typical for Americancities, can be clearly seen in this image, as well as highway 95 (upper left to lower right), highway15 (center to upper right), and the mountains surrounding Las Vegas. The high subsidence rates inthe subsidence bowls can also clearly be identified. Figure 4 shows the seasonal component.Clearly, the estimated amplitude of the seasonal displacement is significant for the central subsidence bowl, i.e., 10 mm. Also the phase offset of the seasonal displacement has been estimated.The average estimated offset is 0.5 year at the positions with the largest amplitude. Since the master image is acquired June 13, the maximum (relative uplift) of the seasonal term thus occurs aroundMarch and the minimum (additional subsidence) around September.

114Bamler et al.Figure 1: Estimated linear displacement rates at finally selected points using data corrected for atmospheric signal.Plotted in the range [-10, 10] mm/y. Subsidence rates near the city of Gardanne of more than 10 mm/y (red) are detected.

Bamler et al.115Figure 2: Displacement time series for a point near (left) and a point in (right) the subsidence area. The estimated lineof-sight displacement rates of 2.0 mm/y and 10.5 mm/y, respectively, are indicated by the red lines. The error barsshow the estimated one-sigma error of 3 mm. On the bottom, the amplitude time series of the PS points is given indB.Figure 3: Estimated average displacement rate for the Las Vegas area between 1992 and 2000. Red corresponds to 20mm/y subsidence and blue to 20 mm/y uplift. Large subsidence bowls are clearly visible, caused by ground water extraction.